2 different textures are overlaying (Blender Render)
You were correct in adding geometry. However, when vertices/faces share the exact same space in Blender, you will get artifacts that are drawn all of the mesh.

To fix this, simply adjust the geometry so it doesn't share the same space. You can scale it in (with S or AltS) or delete the inside geometry, add a solidify modifier and set the material index offset to the material index of the inside material:



(The material index is zero-based. Thus, the selected materials index is 1)



(Set the material index to 1)

Result:



(Object cut in half for demonstration purposes)